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Uncertainty relations state that there exist certain incompatiblemeasurements, to which the outcomes cannot be simultaneously predicted. Whilethe exact incompatibility of quantum measurements dictated by such uncertaintyrelations can be inferred from the mathematical formalism of quantum theory,the question remains whether there is any more fundamental reason for theuncertainty relations to have this exact form. What, if any, would be theoperational consequences if we were able to go beyond any of these uncertaintyrelations? We give a strong argument that justifies uncertainty relations inquantum theory by showing that violating them implies that it is also possibleto violate the second law of thermodynamics. More precisely, we show thatviolating the uncertainty relations in quantum mechanics leads to athermodynamic cycle with positive net work gain, which is very unlikely toexist in nature.

A violation of the uncertainty principle implies a violation of the second law of thermodynamics